{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LBR3U2UWEVYECQAA4ZTSIORY3T","short_pith_number":"pith:LBR3U2UW","canonical_record":{"source":{"id":"1101.0775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-04T17:37:23Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"e831d7fc986369502b4d2b6fbb370b57389ebfb3c64fd479a4b9c1f0125eb4ea","abstract_canon_sha256":"79a9626e96a2d85da60aa752aed201999de2b43e6d88239c51d09a8f5fcdf4b7"},"schema_version":"1.0"},"canonical_sha256":"5863ba6a962570414000e667243a38dce22e17a5f9551b90dcfdef223a627a24","source":{"kind":"arxiv","id":"1101.0775","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0775","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0775v1","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0775","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"pith_short_12","alias_value":"LBR3U2UWEVYE","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LBR3U2UWEVYECQAA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LBR3U2UW","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LBR3U2UWEVYECQAA4ZTSIORY3T","target":"record","payload":{"canonical_record":{"source":{"id":"1101.0775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-04T17:37:23Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"e831d7fc986369502b4d2b6fbb370b57389ebfb3c64fd479a4b9c1f0125eb4ea","abstract_canon_sha256":"79a9626e96a2d85da60aa752aed201999de2b43e6d88239c51d09a8f5fcdf4b7"},"schema_version":"1.0"},"canonical_sha256":"5863ba6a962570414000e667243a38dce22e17a5f9551b90dcfdef223a627a24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:01.419164Z","signature_b64":"F5Ea/jJx/JOVJ9Fz56gVhunMKgx/CutCJmpZkb+ldOl/YPY9SxyT0mMWlACQC5jbdKNKsYnQIzB5VzoDlIK2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5863ba6a962570414000e667243a38dce22e17a5f9551b90dcfdef223a627a24","last_reissued_at":"2026-05-18T04:32:01.418458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:01.418458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.0775","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":"2026-05-18T04:32:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bf8XGNFHTRp5lRxfZWbQJRd9/z3SmDQWiWYEIWLswcs33CftCQ/Hsgy7gyFoslzGCKpD3L5kfYE+Nm2a5ziMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:10:34.297797Z"},"content_sha256":"65ed93ba38838231ef68c3c82e82c8dfe7bad960b5bdab605bc2942954279964","schema_version":"1.0","event_id":"sha256:65ed93ba38838231ef68c3c82e82c8dfe7bad960b5bdab605bc2942954279964"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LBR3U2UWEVYECQAA4ZTSIORY3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Percolate or die: Multi-percolation decides the struggle between competing innovations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"physics.soc-ph","authors_text":"Carlos P. Roca, Dirk Helbing, Moez Draief","submitted_at":"2011-01-04T17:37:23Z","abstract_excerpt":"Competition is one of the most fundamental phenomena in physics, biology and economics. Recent studies of the competition between innovations have highlighted the influence of switching costs and interaction networks, but the problem is still puzzling. We introduce a model that reveals a novel multi-percolation process, which governs the struggle of innovations trying to penetrate a market. We find that innovations thrive as long as they percolate in a population, and one becomes dominant when it is the only one that percolates. Besides offering a theoretical framework to understand the diffus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0775","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":""},"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":"2026-05-18T04:32:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VMIMrXJPBISQBAYMgs2X9tjvpHJsKvPt4aNn8LOumYtJ2I3NYNewvLs7cGZbs0GqtNM7JiZt985v9VHoN0FOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:10:34.298135Z"},"content_sha256":"f9ff0f9ebf6e45dc0016360808dbdff12d0156b9306fa3da6092367427b7151c","schema_version":"1.0","event_id":"sha256:f9ff0f9ebf6e45dc0016360808dbdff12d0156b9306fa3da6092367427b7151c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBR3U2UWEVYECQAA4ZTSIORY3T/bundle.json","state_url":"https://pith.science/pith/LBR3U2UWEVYECQAA4ZTSIORY3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBR3U2UWEVYECQAA4ZTSIORY3T/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":"2026-06-04T01:10:34Z","links":{"resolver":"https://pith.science/pith/LBR3U2UWEVYECQAA4ZTSIORY3T","bundle":"https://pith.science/pith/LBR3U2UWEVYECQAA4ZTSIORY3T/bundle.json","state":"https://pith.science/pith/LBR3U2UWEVYECQAA4ZTSIORY3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBR3U2UWEVYECQAA4ZTSIORY3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LBR3U2UWEVYECQAA4ZTSIORY3T","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":"79a9626e96a2d85da60aa752aed201999de2b43e6d88239c51d09a8f5fcdf4b7","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-04T17:37:23Z","title_canon_sha256":"e831d7fc986369502b4d2b6fbb370b57389ebfb3c64fd479a4b9c1f0125eb4ea"},"schema_version":"1.0","source":{"id":"1101.0775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0775","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0775v1","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0775","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"pith_short_12","alias_value":"LBR3U2UWEVYE","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LBR3U2UWEVYECQAA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LBR3U2UW","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:f9ff0f9ebf6e45dc0016360808dbdff12d0156b9306fa3da6092367427b7151c","target":"graph","created_at":"2026-05-18T04:32:01Z","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"},"paper":{"abstract_excerpt":"Competition is one of the most fundamental phenomena in physics, biology and economics. Recent studies of the competition between innovations have highlighted the influence of switching costs and interaction networks, but the problem is still puzzling. We introduce a model that reveals a novel multi-percolation process, which governs the struggle of innovations trying to penetrate a market. We find that innovations thrive as long as they percolate in a population, and one becomes dominant when it is the only one that percolates. Besides offering a theoretical framework to understand the diffus","authors_text":"Carlos P. Roca, Dirk Helbing, Moez Draief","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-04T17:37:23Z","title":"Percolate or die: Multi-percolation decides the struggle between competing innovations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0775","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":"sha256:65ed93ba38838231ef68c3c82e82c8dfe7bad960b5bdab605bc2942954279964","target":"record","created_at":"2026-05-18T04:32:01Z","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":"79a9626e96a2d85da60aa752aed201999de2b43e6d88239c51d09a8f5fcdf4b7","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-04T17:37:23Z","title_canon_sha256":"e831d7fc986369502b4d2b6fbb370b57389ebfb3c64fd479a4b9c1f0125eb4ea"},"schema_version":"1.0","source":{"id":"1101.0775","kind":"arxiv","version":1}},"canonical_sha256":"5863ba6a962570414000e667243a38dce22e17a5f9551b90dcfdef223a627a24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5863ba6a962570414000e667243a38dce22e17a5f9551b90dcfdef223a627a24","first_computed_at":"2026-05-18T04:32:01.418458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:01.418458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F5Ea/jJx/JOVJ9Fz56gVhunMKgx/CutCJmpZkb+ldOl/YPY9SxyT0mMWlACQC5jbdKNKsYnQIzB5VzoDlIK2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:01.419164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65ed93ba38838231ef68c3c82e82c8dfe7bad960b5bdab605bc2942954279964","sha256:f9ff0f9ebf6e45dc0016360808dbdff12d0156b9306fa3da6092367427b7151c"],"state_sha256":"0894a2f805f3de7dbbd132c9753aa6acb26cc7c71ed2bdbc5b2f46abb3617fd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QTk1/tkPOfHXAoTnxARMjuaKxfYrXwBKugVAaomhCw1ZsECWdpD8aI3xIfTyhSBX6Ef3UdIQj8OhrdoZAvnRBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T01:10:34.300070Z","bundle_sha256":"422d62d3117af0cec74093c57e5824706563a3a712390cec9c953897f7d58ab5"}}