{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HTXXLTZ4AM5W274CVOAAB2IVV7","short_pith_number":"pith:HTXXLTZ4","canonical_record":{"source":{"id":"1206.2495","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-12T11:35:50Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"2dfc3e976dfe17e2b705a36e99379717fc5e325b793540a9403d605731b61331","abstract_canon_sha256":"695d8c8910373b7b3540778dc3a3a15f452e16933b86580f46af9376583b8db4"},"schema_version":"1.0"},"canonical_sha256":"3cef75cf3c033b6d7f82ab8000e915afce0d272f6394c7fc1b57e6094e7030df","source":{"kind":"arxiv","id":"1206.2495","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2495","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2495v3","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2495","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"HTXXLTZ4AM5W","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HTXXLTZ4AM5W274C","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HTXXLTZ4","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HTXXLTZ4AM5W274CVOAAB2IVV7","target":"record","payload":{"canonical_record":{"source":{"id":"1206.2495","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-12T11:35:50Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"2dfc3e976dfe17e2b705a36e99379717fc5e325b793540a9403d605731b61331","abstract_canon_sha256":"695d8c8910373b7b3540778dc3a3a15f452e16933b86580f46af9376583b8db4"},"schema_version":"1.0"},"canonical_sha256":"3cef75cf3c033b6d7f82ab8000e915afce0d272f6394c7fc1b57e6094e7030df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:28.529301Z","signature_b64":"REc+C9xylQVAFW8gq321ea6BmPNbHAQi49KkfOs9Befz9Y7atgssKODPJcw2fvCVQ5euPuA9XU8z9sM/vRNHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cef75cf3c033b6d7f82ab8000e915afce0d272f6394c7fc1b57e6094e7030df","last_reissued_at":"2026-05-18T03:39:28.528519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:28.528519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.2495","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v9F10HVmPU2sUuxHxGPdZhKfwtcsDARsaIpUnVCtccBFzPxmsGERm3BsmLHvFF2FTZBzWhxO2wkPTdnlUzpkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:46:38.061986Z"},"content_sha256":"a2497948c021a565c43d8796a9de9fb792149ab7ab516ba5189d62d74eb7bdfa","schema_version":"1.0","event_id":"sha256:a2497948c021a565c43d8796a9de9fb792149ab7ab516ba5189d62d74eb7bdfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HTXXLTZ4AM5W274CVOAAB2IVV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion in sparse networks: linear to semi-linear crossover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cond-mat.stat-mech","authors_text":"Doron Cohen, Yaron de Leeuw","submitted_at":"2012-06-12T11:35:50Z","abstract_excerpt":"We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension it is well known that $D$ can display an abrupt percolation-like transition from diffusion ($D>0$) to sub-diffusion (D=0). A question arises whether such a transition happens in higher dimensions. Numerically $D$ can be evaluated using a resistor network calculation, or optionally it can be deduced from the spectral properties of the system. Contrary to a r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2495","kind":"arxiv","version":3},"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":"2026-05-18T03:39:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J1ss0U1+W6q9VB5ZK56m2nKngtpmCwFERQ2LFO4taWI4T+E6024G+XQc1zapNYrr6wQaA/vucrKdAX/D+MOtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:46:38.062351Z"},"content_sha256":"835291396ffc0eb1895f39efd35a19cbadf06a8c8cdad2493c2940de3408e8e0","schema_version":"1.0","event_id":"sha256:835291396ffc0eb1895f39efd35a19cbadf06a8c8cdad2493c2940de3408e8e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTXXLTZ4AM5W274CVOAAB2IVV7/bundle.json","state_url":"https://pith.science/pith/HTXXLTZ4AM5W274CVOAAB2IVV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTXXLTZ4AM5W274CVOAAB2IVV7/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":"2026-06-04T04:46:38Z","links":{"resolver":"https://pith.science/pith/HTXXLTZ4AM5W274CVOAAB2IVV7","bundle":"https://pith.science/pith/HTXXLTZ4AM5W274CVOAAB2IVV7/bundle.json","state":"https://pith.science/pith/HTXXLTZ4AM5W274CVOAAB2IVV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTXXLTZ4AM5W274CVOAAB2IVV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HTXXLTZ4AM5W274CVOAAB2IVV7","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":"695d8c8910373b7b3540778dc3a3a15f452e16933b86580f46af9376583b8db4","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-12T11:35:50Z","title_canon_sha256":"2dfc3e976dfe17e2b705a36e99379717fc5e325b793540a9403d605731b61331"},"schema_version":"1.0","source":{"id":"1206.2495","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2495","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2495v3","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2495","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"HTXXLTZ4AM5W","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HTXXLTZ4AM5W274C","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HTXXLTZ4","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:835291396ffc0eb1895f39efd35a19cbadf06a8c8cdad2493c2940de3408e8e0","target":"graph","created_at":"2026-05-18T03:39:28Z","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 consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension it is well known that $D$ can display an abrupt percolation-like transition from diffusion ($D>0$) to sub-diffusion (D=0). A question arises whether such a transition happens in higher dimensions. Numerically $D$ can be evaluated using a resistor network calculation, or optionally it can be deduced from the spectral properties of the system. Contrary to a r","authors_text":"Doron Cohen, Yaron de Leeuw","cross_cats":["cond-mat.mes-hall"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-12T11:35:50Z","title":"Diffusion in sparse networks: linear to semi-linear crossover"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2495","kind":"arxiv","version":3},"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:a2497948c021a565c43d8796a9de9fb792149ab7ab516ba5189d62d74eb7bdfa","target":"record","created_at":"2026-05-18T03:39:28Z","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":"695d8c8910373b7b3540778dc3a3a15f452e16933b86580f46af9376583b8db4","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-12T11:35:50Z","title_canon_sha256":"2dfc3e976dfe17e2b705a36e99379717fc5e325b793540a9403d605731b61331"},"schema_version":"1.0","source":{"id":"1206.2495","kind":"arxiv","version":3}},"canonical_sha256":"3cef75cf3c033b6d7f82ab8000e915afce0d272f6394c7fc1b57e6094e7030df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cef75cf3c033b6d7f82ab8000e915afce0d272f6394c7fc1b57e6094e7030df","first_computed_at":"2026-05-18T03:39:28.528519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:28.528519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"REc+C9xylQVAFW8gq321ea6BmPNbHAQi49KkfOs9Befz9Y7atgssKODPJcw2fvCVQ5euPuA9XU8z9sM/vRNHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:28.529301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2495","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2497948c021a565c43d8796a9de9fb792149ab7ab516ba5189d62d74eb7bdfa","sha256:835291396ffc0eb1895f39efd35a19cbadf06a8c8cdad2493c2940de3408e8e0"],"state_sha256":"5de164a49d60f8c923e4e5b1286a49d0f51aee8c947c5eec00997e6fcf516a76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a+Uxi7klghku7tRhmHxFx4al1O5vbxtuNemRhRdI/brp/wQUuGkoD4sioHcQdaU1MdUeoLVE538yEc2K5zUNAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:46:38.065479Z","bundle_sha256":"938fbd3d293345b1817465a29d4d06975257778127bed6207c7e6f627c687c4d"}}