{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AMXGUA2HWDQKKVTZZWDCO3RV5B","short_pith_number":"pith:AMXGUA2H","canonical_record":{"source":{"id":"1411.0715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-03T22:00:48Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"334d2b4a23712239bddc55f317daf04499dda0747999aa0f19a72ae7f3fd95c4","abstract_canon_sha256":"6c3dadffea9b249161c83edae514e0d31a79d92ba774061ee8ac7441d2fd87b3"},"schema_version":"1.0"},"canonical_sha256":"032e6a0347b0e0a55679cd86276e35e85e3c9aa973a31eda58eb7bd42df7c1d7","source":{"kind":"arxiv","id":"1411.0715","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0715","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0715v1","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0715","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"AMXGUA2HWDQK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AMXGUA2HWDQKKVTZ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AMXGUA2H","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AMXGUA2HWDQKKVTZZWDCO3RV5B","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-03T22:00:48Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"334d2b4a23712239bddc55f317daf04499dda0747999aa0f19a72ae7f3fd95c4","abstract_canon_sha256":"6c3dadffea9b249161c83edae514e0d31a79d92ba774061ee8ac7441d2fd87b3"},"schema_version":"1.0"},"canonical_sha256":"032e6a0347b0e0a55679cd86276e35e85e3c9aa973a31eda58eb7bd42df7c1d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:38.388271Z","signature_b64":"2EhtCTNdw7fhABkSUKxhBR1iZjcU/bOn4msxTAM8KILrqQP34E9o6+ivBKgKjCLkL3GiKS16IXMm4gXx7PreBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"032e6a0347b0e0a55679cd86276e35e85e3c9aa973a31eda58eb7bd42df7c1d7","last_reissued_at":"2026-05-18T02:38:38.387904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:38.387904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0715","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":"2026-05-18T02:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xh21l1F/Ap6hvrqEGw3IeXaHMDDQVJp5iFuEJ75gM2Mbldj8AR+ZH9RURso9a3VgMqihYFv4GrURZaOlTwJiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:24:40.530035Z"},"content_sha256":"fb94b420756afaa31ee18e44ee218c77b3264c154a64768fab342812752f80b0","schema_version":"1.0","event_id":"sha256:fb94b420756afaa31ee18e44ee218c77b3264c154a64768fab342812752f80b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AMXGUA2HWDQKKVTZZWDCO3RV5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond the Steady-State: Analytical Study of Network Growth at Arbitrary Times, for Arbitrary Initial Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Babak Fotouhi","submitted_at":"2014-11-03T22:00:48Z","abstract_excerpt":"In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the infinite-size limit). Consequently, empirical studies also seek to verify the steady-state prediction in real data. The caveat concomitant with confining the analysis to this time regime is that no real system has infinite size; most real growing networks are far from the steady state. This underlines the importance of finite-size analysis. In this paper, we consider "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0715","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":"2026-05-18T02:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1FfUtr1anliaMB8HmHtzsqF228piYmLLKps2zjKKXbnNo3L3i5elv4+epPnAKcaX9qnZAgKHeEvqnM1Vpj5YAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:24:40.530758Z"},"content_sha256":"a10fa7b3c46aa85c5f6f87e633b444dc40ee07abe84e12d76566b93bdf1cb3e5","schema_version":"1.0","event_id":"sha256:a10fa7b3c46aa85c5f6f87e633b444dc40ee07abe84e12d76566b93bdf1cb3e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMXGUA2HWDQKKVTZZWDCO3RV5B/bundle.json","state_url":"https://pith.science/pith/AMXGUA2HWDQKKVTZZWDCO3RV5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMXGUA2HWDQKKVTZZWDCO3RV5B/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":"2026-05-25T19:24:40Z","links":{"resolver":"https://pith.science/pith/AMXGUA2HWDQKKVTZZWDCO3RV5B","bundle":"https://pith.science/pith/AMXGUA2HWDQKKVTZZWDCO3RV5B/bundle.json","state":"https://pith.science/pith/AMXGUA2HWDQKKVTZZWDCO3RV5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMXGUA2HWDQKKVTZZWDCO3RV5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AMXGUA2HWDQKKVTZZWDCO3RV5B","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":"6c3dadffea9b249161c83edae514e0d31a79d92ba774061ee8ac7441d2fd87b3","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-03T22:00:48Z","title_canon_sha256":"334d2b4a23712239bddc55f317daf04499dda0747999aa0f19a72ae7f3fd95c4"},"schema_version":"1.0","source":{"id":"1411.0715","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0715","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0715v1","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0715","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"AMXGUA2HWDQK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AMXGUA2HWDQKKVTZ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AMXGUA2H","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:a10fa7b3c46aa85c5f6f87e633b444dc40ee07abe84e12d76566b93bdf1cb3e5","target":"graph","created_at":"2026-05-18T02:38:38Z","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":"In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the infinite-size limit). Consequently, empirical studies also seek to verify the steady-state prediction in real data. The caveat concomitant with confining the analysis to this time regime is that no real system has infinite size; most real growing networks are far from the steady state. This underlines the importance of finite-size analysis. In this paper, we consider ","authors_text":"Babak Fotouhi","cross_cats":["cond-mat.stat-mech","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-03T22:00:48Z","title":"Beyond the Steady-State: Analytical Study of Network Growth at Arbitrary Times, for Arbitrary Initial Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0715","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:fb94b420756afaa31ee18e44ee218c77b3264c154a64768fab342812752f80b0","target":"record","created_at":"2026-05-18T02:38:38Z","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":"6c3dadffea9b249161c83edae514e0d31a79d92ba774061ee8ac7441d2fd87b3","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-03T22:00:48Z","title_canon_sha256":"334d2b4a23712239bddc55f317daf04499dda0747999aa0f19a72ae7f3fd95c4"},"schema_version":"1.0","source":{"id":"1411.0715","kind":"arxiv","version":1}},"canonical_sha256":"032e6a0347b0e0a55679cd86276e35e85e3c9aa973a31eda58eb7bd42df7c1d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"032e6a0347b0e0a55679cd86276e35e85e3c9aa973a31eda58eb7bd42df7c1d7","first_computed_at":"2026-05-18T02:38:38.387904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:38.387904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2EhtCTNdw7fhABkSUKxhBR1iZjcU/bOn4msxTAM8KILrqQP34E9o6+ivBKgKjCLkL3GiKS16IXMm4gXx7PreBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:38.388271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0715","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb94b420756afaa31ee18e44ee218c77b3264c154a64768fab342812752f80b0","sha256:a10fa7b3c46aa85c5f6f87e633b444dc40ee07abe84e12d76566b93bdf1cb3e5"],"state_sha256":"ee457f5bdfe6a2f25121ef5f223fcd7f255cf9da2a219f10a2d72e2f6a367f86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mtvQPmmXMEyUCptTqu7sQ6eOsoY7p+0wUUU13fNZM2ki9BYht/jxKRqs86W9acn3fUwh/fSf/57bLVQsLMyvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:24:40.534646Z","bundle_sha256":"3151b55693ea50cc429914a950eb0f5116dc6fc688e51099a712d36d0ecc4a24"}}