{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UR4FYQ2MORUSBN4ZORBZV4JJFC","short_pith_number":"pith:UR4FYQ2M","canonical_record":{"source":{"id":"1108.2854","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-08-14T10:05:44Z","cross_cats_sorted":["cs.NI","physics.data-an"],"title_canon_sha256":"97e648e5d039bc3bff966d5c8adcd178a8a59c9c053fb8f257e6e7a0c3cf5756","abstract_canon_sha256":"0f9f3fb211567ce6d1cb4ac3ed069a5cea7c454e417ddb9bc906490a18142529"},"schema_version":"1.0"},"canonical_sha256":"a4785c434c746920b79974439af12928afe7380aca069faaf8b7a75e5d7d5af6","source":{"kind":"arxiv","id":"1108.2854","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2854","created_at":"2026-05-18T02:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2854v2","created_at":"2026-05-18T02:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2854","created_at":"2026-05-18T02:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"UR4FYQ2MORUS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UR4FYQ2MORUSBN4Z","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UR4FYQ2M","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UR4FYQ2MORUSBN4ZORBZV4JJFC","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2854","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-08-14T10:05:44Z","cross_cats_sorted":["cs.NI","physics.data-an"],"title_canon_sha256":"97e648e5d039bc3bff966d5c8adcd178a8a59c9c053fb8f257e6e7a0c3cf5756","abstract_canon_sha256":"0f9f3fb211567ce6d1cb4ac3ed069a5cea7c454e417ddb9bc906490a18142529"},"schema_version":"1.0"},"canonical_sha256":"a4785c434c746920b79974439af12928afe7380aca069faaf8b7a75e5d7d5af6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:41.840064Z","signature_b64":"2+uAn5NmT+H0VALBf2BgRBjk9QigDMrnB8gBHTCsVYymELrpVn3uPjWubEUfifmLipXlTNsw6vmGhXkPtAVhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4785c434c746920b79974439af12928afe7380aca069faaf8b7a75e5d7d5af6","last_reissued_at":"2026-05-18T02:21:41.839649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:41.839649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2854","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yJFuz0J0v2vn0cH0yYkhGbSQkh6iS7spgyXeLt2G9O0QBg3krpkaVZD7R/Qoh4EhtlGlgQMvMLEFrBMlw5PlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:18:33.273539Z"},"content_sha256":"1cb1390cae271988b80e63e7e4d2fd9c7707d22e5d372673e8103703fc349d47","schema_version":"1.0","event_id":"sha256:1cb1390cae271988b80e63e7e4d2fd9c7707d22e5d372673e8103703fc349d47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UR4FYQ2MORUSBN4ZORBZV4JJFC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transmission of packets on a hierarchical network: Statistics and explosive percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","physics.data-an"],"primary_cat":"cond-mat.stat-mech","authors_text":"Ajay Deep Kachhvah, Neelima Gupte","submitted_at":"2011-08-14T10:05:44Z","abstract_excerpt":"We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell - Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different networ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2854","kind":"arxiv","version":2},"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":"2026-05-18T02:21:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e1qoV0QanPD8QT++OYJ2Vrzwq8jfmYdvn596qU2ZOL2OfwmDS3NGKI9Hcy/kjxXITXBhEHFcyJrvaWw1ZFnVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:18:33.273889Z"},"content_sha256":"0017e90d576c7d510bd989f9ec9b6a6d72ffa278bfafbd200bf559313b049f55","schema_version":"1.0","event_id":"sha256:0017e90d576c7d510bd989f9ec9b6a6d72ffa278bfafbd200bf559313b049f55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UR4FYQ2MORUSBN4ZORBZV4JJFC/bundle.json","state_url":"https://pith.science/pith/UR4FYQ2MORUSBN4ZORBZV4JJFC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UR4FYQ2MORUSBN4ZORBZV4JJFC/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":"2026-06-03T17:18:33Z","links":{"resolver":"https://pith.science/pith/UR4FYQ2MORUSBN4ZORBZV4JJFC","bundle":"https://pith.science/pith/UR4FYQ2MORUSBN4ZORBZV4JJFC/bundle.json","state":"https://pith.science/pith/UR4FYQ2MORUSBN4ZORBZV4JJFC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UR4FYQ2MORUSBN4ZORBZV4JJFC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UR4FYQ2MORUSBN4ZORBZV4JJFC","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":"0f9f3fb211567ce6d1cb4ac3ed069a5cea7c454e417ddb9bc906490a18142529","cross_cats_sorted":["cs.NI","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-08-14T10:05:44Z","title_canon_sha256":"97e648e5d039bc3bff966d5c8adcd178a8a59c9c053fb8f257e6e7a0c3cf5756"},"schema_version":"1.0","source":{"id":"1108.2854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2854","created_at":"2026-05-18T02:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2854v2","created_at":"2026-05-18T02:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2854","created_at":"2026-05-18T02:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"UR4FYQ2MORUS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UR4FYQ2MORUSBN4Z","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UR4FYQ2M","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:0017e90d576c7d510bd989f9ec9b6a6d72ffa278bfafbd200bf559313b049f55","target":"graph","created_at":"2026-05-18T02:21:41Z","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":"We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell - Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different networ","authors_text":"Ajay Deep Kachhvah, Neelima Gupte","cross_cats":["cs.NI","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-08-14T10:05:44Z","title":"Transmission of packets on a hierarchical network: Statistics and explosive percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2854","kind":"arxiv","version":2},"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":"sha256:1cb1390cae271988b80e63e7e4d2fd9c7707d22e5d372673e8103703fc349d47","target":"record","created_at":"2026-05-18T02:21:41Z","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":"0f9f3fb211567ce6d1cb4ac3ed069a5cea7c454e417ddb9bc906490a18142529","cross_cats_sorted":["cs.NI","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-08-14T10:05:44Z","title_canon_sha256":"97e648e5d039bc3bff966d5c8adcd178a8a59c9c053fb8f257e6e7a0c3cf5756"},"schema_version":"1.0","source":{"id":"1108.2854","kind":"arxiv","version":2}},"canonical_sha256":"a4785c434c746920b79974439af12928afe7380aca069faaf8b7a75e5d7d5af6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4785c434c746920b79974439af12928afe7380aca069faaf8b7a75e5d7d5af6","first_computed_at":"2026-05-18T02:21:41.839649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:41.839649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2+uAn5NmT+H0VALBf2BgRBjk9QigDMrnB8gBHTCsVYymELrpVn3uPjWubEUfifmLipXlTNsw6vmGhXkPtAVhCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:41.840064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cb1390cae271988b80e63e7e4d2fd9c7707d22e5d372673e8103703fc349d47","sha256:0017e90d576c7d510bd989f9ec9b6a6d72ffa278bfafbd200bf559313b049f55"],"state_sha256":"464860e5be944bd3dbcac23f818720eea21a6a4229062777331198c8646d9f45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3temqf7Js+Z9TJUW12mAYJ4BWltavxIO/u9QaUWdht8s4QbQIS5B7+vTMw0Xu7PvYFa1l0A7Pj7h+5uq9J/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:18:33.275871Z","bundle_sha256":"ced30c117dc4130d01cdda45016ebc9f72c4f9088fee16b0aa2f1d96ef69572c"}}