{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:IRFHOCCTMPZUVLT5KI6ORCN6SM","short_pith_number":"pith:IRFHOCCT","canonical_record":{"source":{"id":"2011.09268","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"econ.TH","submitted_at":"2020-11-17T09:39:52Z","cross_cats_sorted":["cs.GT","cs.SI","cs.SY","eess.SY"],"title_canon_sha256":"109082748a01bc5a35dcfaa18f40a33abd90855d7a7f3e37e9ddd565773e13c4","abstract_canon_sha256":"74c0ab51f9a50c522dd006848c72cf0c572baadf3689f9563c8701371b3f1c53"},"schema_version":"1.0"},"canonical_sha256":"444a77085363f34aae7d523ce889be930ad586828cc6f3ddb167a0ea05933c66","source":{"kind":"arxiv","id":"2011.09268","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09268","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09268v1","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09268","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"IRFHOCCTMPZU","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_16","alias_value":"IRFHOCCTMPZUVLT5","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_8","alias_value":"IRFHOCCT","created_at":"2026-07-05T01:52:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:IRFHOCCTMPZUVLT5KI6ORCN6SM","target":"record","payload":{"canonical_record":{"source":{"id":"2011.09268","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"econ.TH","submitted_at":"2020-11-17T09:39:52Z","cross_cats_sorted":["cs.GT","cs.SI","cs.SY","eess.SY"],"title_canon_sha256":"109082748a01bc5a35dcfaa18f40a33abd90855d7a7f3e37e9ddd565773e13c4","abstract_canon_sha256":"74c0ab51f9a50c522dd006848c72cf0c572baadf3689f9563c8701371b3f1c53"},"schema_version":"1.0"},"canonical_sha256":"444a77085363f34aae7d523ce889be930ad586828cc6f3ddb167a0ea05933c66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:42.340245Z","signature_b64":"S/tYBbX6Qg95gcPhPLiekUSfRW+XGqLjg32THBtZDbjb+GcFKn9kOGHQDCd2r+iuEU+vqJqQBLWiwN5IBb6cDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"444a77085363f34aae7d523ce889be930ad586828cc6f3ddb167a0ea05933c66","last_reissued_at":"2026-07-05T01:52:42.339797Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:42.339797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.09268","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zqxbz+3eR3Hyq+lkCIqOzpwhx0vI2CJEvWJZqIYZGiOfrqJn0nakCg0JsvW16+OOXJ4hcCUENolBsKSu+oUaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-15T21:06:11.233275Z"},"content_sha256":"2b54686710594047e89591ef45a9d806c80f50985435d4b2e4f2a47f78c40e8f","schema_version":"1.0","event_id":"sha256:2b54686710594047e89591ef45a9d806c80f50985435d4b2e4f2a47f78c40e8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:IRFHOCCTMPZUVLT5KI6ORCN6SM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Allocating marketing resources over social networks: A long-term analysis","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.GT","cs.SI","cs.SY","eess.SY"],"primary_cat":"econ.TH","authors_text":"Irinel-Constantin Morarescu, Julien Mounthanyvong, Samson Lasaulce, Vineeth S. Varma","submitted_at":"2020-11-17T09:39:52Z","abstract_excerpt":"In this paper, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows a hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed recently in [1], we prove that although the marketers are in competition and therefore create tension in the network, the network reaches a consensus. Exploiting this key result, we propose a coopetition marketing strategy which combines the one-shot Nash equilibrium actions and a policy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09268","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.09268/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2XRJHIETR4pvrkFJi7GXHrnQwdrsU+z1bSWCzV3+NKNaU8nA03BhvI5bn/2o71KQaOVm1PPfTAPNMOPXs8fCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-15T21:06:11.233681Z"},"content_sha256":"0cfcde484a88b04063e3fa15a5837b200fa1e861f91b2560e91a221608a4d5c2","schema_version":"1.0","event_id":"sha256:0cfcde484a88b04063e3fa15a5837b200fa1e861f91b2560e91a221608a4d5c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IRFHOCCTMPZUVLT5KI6ORCN6SM/bundle.json","state_url":"https://pith.science/pith/IRFHOCCTMPZUVLT5KI6ORCN6SM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IRFHOCCTMPZUVLT5KI6ORCN6SM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-15T21:06:11Z","links":{"resolver":"https://pith.science/pith/IRFHOCCTMPZUVLT5KI6ORCN6SM","bundle":"https://pith.science/pith/IRFHOCCTMPZUVLT5KI6ORCN6SM/bundle.json","state":"https://pith.science/pith/IRFHOCCTMPZUVLT5KI6ORCN6SM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IRFHOCCTMPZUVLT5KI6ORCN6SM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:IRFHOCCTMPZUVLT5KI6ORCN6SM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"74c0ab51f9a50c522dd006848c72cf0c572baadf3689f9563c8701371b3f1c53","cross_cats_sorted":["cs.GT","cs.SI","cs.SY","eess.SY"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"econ.TH","submitted_at":"2020-11-17T09:39:52Z","title_canon_sha256":"109082748a01bc5a35dcfaa18f40a33abd90855d7a7f3e37e9ddd565773e13c4"},"schema_version":"1.0","source":{"id":"2011.09268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09268","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09268v1","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09268","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"IRFHOCCTMPZU","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_16","alias_value":"IRFHOCCTMPZUVLT5","created_at":"2026-07-05T01:52:42Z"},{"alias_kind":"pith_short_8","alias_value":"IRFHOCCT","created_at":"2026-07-05T01:52:42Z"}],"graph_snapshots":[{"event_id":"sha256:0cfcde484a88b04063e3fa15a5837b200fa1e861f91b2560e91a221608a4d5c2","target":"graph","created_at":"2026-07-05T01:52:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2011.09268/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows a hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed recently in [1], we prove that although the marketers are in competition and therefore create tension in the network, the network reaches a consensus. Exploiting this key result, we propose a coopetition marketing strategy which combines the one-shot Nash equilibrium actions and a policy ","authors_text":"Irinel-Constantin Morarescu, Julien Mounthanyvong, Samson Lasaulce, Vineeth S. Varma","cross_cats":["cs.GT","cs.SI","cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"econ.TH","submitted_at":"2020-11-17T09:39:52Z","title":"Allocating marketing resources over social networks: A long-term analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09268","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2b54686710594047e89591ef45a9d806c80f50985435d4b2e4f2a47f78c40e8f","target":"record","created_at":"2026-07-05T01:52:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"74c0ab51f9a50c522dd006848c72cf0c572baadf3689f9563c8701371b3f1c53","cross_cats_sorted":["cs.GT","cs.SI","cs.SY","eess.SY"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"econ.TH","submitted_at":"2020-11-17T09:39:52Z","title_canon_sha256":"109082748a01bc5a35dcfaa18f40a33abd90855d7a7f3e37e9ddd565773e13c4"},"schema_version":"1.0","source":{"id":"2011.09268","kind":"arxiv","version":1}},"canonical_sha256":"444a77085363f34aae7d523ce889be930ad586828cc6f3ddb167a0ea05933c66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"444a77085363f34aae7d523ce889be930ad586828cc6f3ddb167a0ea05933c66","first_computed_at":"2026-07-05T01:52:42.339797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:52:42.339797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S/tYBbX6Qg95gcPhPLiekUSfRW+XGqLjg32THBtZDbjb+GcFKn9kOGHQDCd2r+iuEU+vqJqQBLWiwN5IBb6cDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:52:42.340245Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.09268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b54686710594047e89591ef45a9d806c80f50985435d4b2e4f2a47f78c40e8f","sha256:0cfcde484a88b04063e3fa15a5837b200fa1e861f91b2560e91a221608a4d5c2"],"state_sha256":"cb9fed9b3f87bc76d01f2216d48a2b36fa877e6921b1f1763078b7531c2e4bfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NpEUQUhhTiNsgOo0OId3njthCMOJ3PAWIxZyCLt4Ir19bkAjhTbON6CCybIfgpTVVeRGsDuCgpO5kaOmhAtLDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-15T21:06:11.235934Z","bundle_sha256":"c5108458cf3581edbf6ef868f43f9234102ad332d2eddc31a54b006d19579572"}}